Reliability-based design of R/C water tank structures under seismic action

Based on a reliability level 2 method, a procedure is proposed to design reinforced concrete structures for elevated tanks subjected to seismic action, with a specified probability of failure in a 50-year design life. To evaluate the probability of failure the ultimate limit state is obtained when the top column displacement demanded by the earthquake, a random variable, reaches the allowable displacement, which is here treated as deterministic. The seismic action is characterized probabilistically by the power spectral density function of the ground acceleration, which is obtained from a design spectrum. The strength and ductility of an annular column section of confined reinforced concrete for cyclic loads are evaluated with design aids. Design charts are made for a given tank capacity and specified seismic zone that allow one to choose different combinations of strength, stiffness and ductility for the same tolerable probability of failure. A step by step method is suggested for the design of the annular column section, choosing finally the most convenient design. The advantage of this methodology is shown through a numerical example.     

Performance-based methodology for assessing seismic vulnerability and capacity of buildings

This paper presents a performance-based methodology for the assessment of seismic vulnerability and capacity of buildings. The vulnerability assessment methodology is based on the HAZUS methodology and the improved capacity- demand-diagram method. The spectral displacement (Sd) of performance points on a capacity curve is used to estimate the damage level of a building. The relationship between Sd and peak ground acceleration (PGA) is established, and then a new vulnerability function is expressed in terms of PGA. Furthermore, the expected value of the seismic capacity index (SCev) is provided to estimate the seismic capacity of buildings based on the probability distribution of damage levels and the corresponding seismic capacity index. The results indicate that the proposed vulnerability methodology is able to assess seismic damage of a large number of building stock directly and quickly following an earthquake. The SCev provides an effective index to measure the seismic capacity of buildings and illustrate the relationship between the seismic capacity of buildings and seismic action. The estimated result is compared with damage surveys of the cities of Dujiangyan and Jiangyou in the M8.0 Wenchuan earthquake, revealing that the methodology is acceptable for seismic risk assessment and decision making. The primary reasons for discrepancies between the estimated results and the damage surveys are discussed.     

Inclusion of P–Δ effect in displacement‐based seismic design of steel moment resisting frames

A procedure for treating the P– Δ effect in the direct displacement‐based seismic design of regular steel moment resisting frames with ideal elastoplastic material behaviour is proposed. A simple formula for the yield displacement amplification factor as a function of ductility and the stability coefficient is derived on the basis of the seismic response of an inelastic single degree‐of‐freedom system taking into account the P– Δ effect. Extensive parametric seismic inelastic analyses of plane moment resisting steel frames result in a simple formula for the dynamic stability coefficient as a function of the number of stories of a frame and the column to beam stiffness ratio. Thus, the P– Δ effect can be easily taken into account in a direct displacement‐based seismic design through the stability coefficient and the yield displacement amplification factor. A simple design example serves to illustrate the application of the proposed method and demonstrate its merits. Copyright © 2007 John Wiley & Sons, Ltd.     

Life‐cycle reliability of RC bridge piers under seismic and airborne chloride hazards

Over the last two decades, the probabilistic assessment of reinforced concrete (RC) structures under seismic hazard has been developed rapidly. However, little attention has been devoted to the assessment of the seismic reliability of corroded structures. For the life‐cycle assessment of RC structures in a marine environment and earthquake‐prone regions, the effect of corrosion due to airborne chlorides on the seismic capacity needs to be taken into consideration. Also, the effect of the type of corrosive environment on the seismic capacity of RC structures has to be quantified. In this paper, the evaluation of the displacement ductility capacity based on the buckling model of longitudinal rebars in corroded RC bridge piers is established, and a novel computational procedure to integrate the probabilistic hazard associated with airborne chlorides into life‐cycle seismic reliability assessment of these piers is proposed. The seismic demand depends on the results of seismic hazard assessment, whereas the deterioration of seismic capacity depends on the hazard associated with airborne chlorides. In an illustrative example, an RC bridge pier was modeled as single degree of freedom (SDOF). The longitudinal rebars buckling of this pier was considered as the sole limit state when estimating its failure probability. The findings show that the life‐cycle reliability of RC bridge piers depends on both the seismic and airborne chloride hazards, and that the cumulative‐time failure probabilities of RC bridge piers located in seismic zones can be dramatically affected by the effect of airborne chlorides. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic reliability of V‐braced frames: Influence of design methodologies

According to the most modern trend, performance‐based seismic design is aimed at the evaluation of the seismic structural reliability defined as the mean annual frequency (MAF) of exceeding a threshold level of damage, i.e. a limit state. The methodology for the evaluation of the MAF of exceeding a limit state is herein applied with reference to concentrically ‘V’‐braced steel frames designed according to different criteria. In particular, two design approaches are examined. The first approach corresponds to the provisions suggested by Eurocode 8 (prEN 1998—Eurocode 8: design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings), while the second approach is based on a rigorous application of capacity design criteria aiming at the control of the failure mode (J. Earthquake Eng. 2008; 12 :1246–1266; J. Earthquake Eng. 2008; 12 :728–759). The aim of the presented work is to focus on the seismic reliability obtained through these design methodologies. The probabilistic performance evaluation is based on an appropriate combination of probabilistic seismic hazard analysis, probabilistic seismic demand analysis (PSDA) and probabilistic seismic capacity analysis. Regarding PSDA, nonlinear dynamic analyses have been carried out in order to obtain the parameters describing the probability distribution laws of demand, conditioned to given values of the earthquake intensity measure. Copyright © 2009 John Wiley & Sons, Ltd.     

Uniform reliability safety format for seismic design of reinforced concrete structures

A safety format is proposed for the flexural design of reinforced concrete members for the combination of seismic and gravity loads, with load and resistance factors which depend on member type, on the value of the target theoretical probability of failure and on the ratio of the load effect due to gravity loads to that due to the nominal value of the seismic action, both obtained by elastic analysis. Safety factors are computed through an advanced Level II reliability procedure, using a limit state inequality between the member rotation ductility supply under monotonic loading and the peak rotation ductility and cyclic energy dissipation demands. Uncertainties considered are: for resistance, the uncertainty of failure under imposed cyclic deformations, and for action, the maximum peak ductility and energy dissipation demands in the structure's lifetime, as obtained through a series of non-linear dynamic analyses of multistorey buildings in 3D. using as input ensembles of bidirectional acceleration time-histories which describe probabilistically the extreme bidirectional seismic action in the structure's lifetime. Computed load and resistance factors are practically independent of the load-effects ratio. The load factor on the seismic action is found to be independent of member type and to increase with the theoretical probability of failure much faster than the elastic spectral value at the structure's fundamental period with probability of exceedance in the structure's lifetime. Simple rules for the dependence of the resistance modification factors on the theoretical failure probability are also derived. As for the computed values of the load factors the moment due to gravity loads is negligible in comparison to the factored seismic moment, a simplified safety checking inequality between the design flexural capacity and a reduced seismic moment is proposed, in which the ratio of the resistance to the load factor plays the role of a force reduction or effective behaviour factor for the member.     

Consistent inelastic design spectra: Hysteretic and input energy

This is the second of two companion papers on inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor. All the spectra are consistent (interrelated and based on the same assumptions). This paper deals with two quantities related to cumulative damage: hysteretic and input energy. The input data for the procedure are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum and the time integral of the square of the ground acceleration ∫a² dt. Simple, approximate expressions for two dimensionless parameters (the parameter γ and the hysteretic to input energy ratio E_HE_I) have been proposed. The parameter 7, which controls the reduction of the deformation capacity of structures due to low-cycle fatigue, depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour and the ground motion characteristics. The ratio E_H/E_I is influenced by damping, the ductility factor and the hysteretic behaviour. Very good approximations to the inelastic spectra for hysteretic and input energy can be derived from the elastic spectrum using the spectra for the reduction factor R, proposed in the companion paper, and the proposed values for γ and E_H/E_I     

Evaluation of displacement coefficient method for seismically retrofitted buildings with various ductility capacities

This research study is aimed at evaluating the accuracy of the displacement coefficient method (DCM) of FEMA 440 and associated nonlinear static procedure (NLSP) for actual buildings with soft story mechanism and various ductility capacities. The DCM and associated NLSP are evaluated using two existing seismically vulnerable buildings with soft story mechanism. The buildings are first retrofitted using a ductile steel‐brace‐link system to represent those with good ductility capacity and then retrofitted with RC squat infill shear panels (SISPs) to represent those with relatively poor ductility capacity. The evaluation of the DCM of FEMA 440 and associated NLSP is then performed by comparing the roof displacements (target displacements), maximum interstory drifts, and maximum plastic hinge rotations of the original and retrofitted buildings obtained from NLSP (at the target displacement level of DCM) with those obtained from nonlinear response history (NRH) analyses for three different seismic performance levels. It is observed that the DCM, and hence, the NLSP fail to accurately predict the NRH analyses results mainly due to uncertainties in the coefficient C₁ of the DCM in the short period range, the inability of the DCM to capture the failure of structural members beyond a certain lateral displacement or plastic rotation limit and associated soft story mechanism. Copyright © 2013 John Wiley & Sons, Ltd.     

Probabilistic seismic demand analysis of controlled steel moment‐resisting frame structures

This paper describes a proposed methodology, referred to as probabilistic seismic control analysis, for the development of probabilistic seismic demand curves for structures with supplemental control devices. The resulting curves may be used to determine the probability that any response measure, whether for a structure or control device, exceeds a pre‐determined allowable limit. This procedure couples conventional probabilistic seismic hazard analysis with non‐linear dynamic structural analyses to provide system specific information. This method is performed by evaluating the performance of specific controlled systems under seismic excitations using the SAC Phase II structures for the Los Angeles region, and three different control‐systems: (i) base isolation; (ii) linear viscous brace dampers; and (iii) active tendon braces. The use of a probabilistic format allows for consideration of structural response over a range of seismic hazards. The resulting annual hazard curves provide a basis for comparison between the different control strategies. Results for these curves indicate that no single control strategy is the most effective at all hazard levels. For example, at low return periods the viscous system has the lowest drift demands. However, at higher return periods, the isolation system becomes the most effective strategy. Copyright © 2002 John Wiley & Sons, Ltd.     

An energy-based procedure for the assessment of seismic capacity of existing frames: Application to RC wide beam systems in Spain

A methodology for assessing the seismic capacity of existing frames in terms of energy is proposed. It estimates the global amount of input energy—in form of a factor AE_IU—and hysteretic energy that the overall structure can dissipate until collapse under earthquake-type loadings. The method requires static pushover analyses to determine the ductility factor and energy shape of an equivalent single-degree-of-freedom system for the first—two or more—modes. The procedure accounts for the relation between the frequency content of the earthquake expected at the site and the dynamic properties of the existing structure. It can be useful for evaluating the possible deficit on energy dissipation capacity of existing structures, and for designing seismic retrofit solutions. Finally, the methodology is applied to reinforced concrete frames with wide beam-column connections representative of existing post-1970 buildings located in the earthquake-prone southern part of Spain.     

Convex model-based calculation of robust seismic fragility curves of isolated continuous girder bridge

The convex model approach is applied to derive the robust seismic fragility curves of a five-span isolated continuous girder bridge with lead rubber bearings (LRB) in China. The uncertainty of structure parameters (the yield force and the post-yield stiffness of LRB, the yield strength of steel bars, etc.) are considered in the convex model, and the uncertainty of earthquake ground motions is also taken into account by selecting 40 earthquake excitations of peak ground acceleration magnitudes ranging from 0.125 to 1.126 g. A 3-D finite element model is employed using the software package OpenSees by considering the nonlinearity in the bridge piers and the isolation bearings. Section ductility of piers and shearing strain isolation bearings are treated as damage indices. The cloud method and convex model approach are used to construct the seismic fragility curves of the bridge components (LRB and bridge piers) and the bridge system, respectively. The numerical results indicate that seismic fragility of the bridge system and bridge components will be underestimated without considering the uncertainty of structural parameters. Therefore, the failure probability P _f,max had better be served as the seismic fragility, especially, the fragility of the bridge system is largely dictated by the fragility of LRB. Finally, the probabilistic seismic performance evaluation of the bridge is carried out according to the structural seismic risk estimate method.     

Seismic vulnerability assessment to slight damage based on experimental modal parameters

The aim of this paper is to adjust behaviour models for each class of structure for vulnerability assessment by using ambient vibration. A simple model based on frequencies, mode shapes and damping, taken from ambient vibrations, allows computation of the response of the structures and comparison of inter‐storey drifts with the limits found in the literature for the slight damage grade, considered here as the limit of elastic behaviour. Two complete methodologies for building fragility curves are proposed: (1) using a multi‐degree of freedom system including higher modes and full seismic ground‐motion and (2) using a single‐degree of freedom model considering the fundamental mode f₀ of the structure and ground‐motion displacement response spectra S_D(f₀). These two methods were applied to the city of Grenoble, where 60 buildings were studied. Fragility curves for slight damage were derived for the various masonry and reinforced concrete classes of buildings. A site‐specific earthquake scenario, taking into account local site conditions, was considered, corresponding to an M_L = 5.5 earthquake at a distance of 15 km. The results show the benefits of using experimental models to reduce variability of the slight damage fragility curve. Moreover, by introducing the experimental modal model of the buildings, it is possible to improve seismic risk assessment at an overall scale (the city) or a local scale (the building) for the first damage grade (slight damage). This level of damage, of great interest for moderate seismic‐prone regions, may contribute to the seismic loss assessment. Copyright © 2011 John Wiley & Sons, Ltd.     

Direct displacement-based seismic design of steel eccentrically braced frame structures

This paper details a direct displacement-based design procedure for steel eccentrically braced frame (EBF) structures and gauges its performance by examining the non-linear dynamic response of a series of case study EBF structures designed using the procedure. Analytical expressions are developed for the storey drift at yield and for the storey drift capacity of EBFs, recognising that in addition to link beam deformations, the brace and column axial deformations can provide important contributions to storey drift components. Case study design results indicate that the ductility capacity of EBF systems will tend to be relatively low, despite the large local ductility capacity offered by well detailed links. In addition, it is found that while the ductility capacity of EBF systems will tend to reduce with height, this is not necessarily negative for seismic performance since the displacement capacity for taller EBF systems will tend to be large. To gauge the performance of the proposed DBD methodology, analytical models of the case study design solutions are subject to non-linear time-history analyses with a set of spectrum-compatible accelerograms. The average displacements and drifts obtained from the NLTH analyses are shown to align well with design values, confirming that the new methodology could provide an effective tool for the seismic design of EBF systems.     

A probabilistic model of seismicity: Kamchatka earthquakes

The catalog of Kamchatka earthquakes is represented as a probability space of three objects {Ω, $ \tilde F $ \tilde F P}. Each earthquake is treated as an outcome ω _i in the space of elementary events Ω whose cardinality for the period under consideration is given by the number of events. In turn, ω _i is characterized by a system of random variables, viz., energy class k_i, latitude φ _i , longitude λ _i , and depth h _i . The time of an outcome has been eliminated from this system in this study. The random variables make up subsets in the set $ \tilde F $ \tilde F and are defined by multivariate distributions, either by the distribution function $ \tilde F $ \tilde F (φ, λ, h, k) or by the probability density f(φ, λ, h, k) based on the earthquake catalog in hand. The probabilities P are treated in the frequency interpretation. Taking the example of a recurrence relation (RR) written down in the form of a power law for probability density f(k), where the initial value of the distribution function f(k ₀) is the basic data [Bogdanov, 2006] rather than the seismic activity A ₀, we proceed to show that for different intervals of coordinates and time the distribution f _elim(k) of an earthquake catalog with the aftershocks eliminated is identical to the distribution f _full(k), which corresponds to the full catalog. It follows from our calculations that f ₀(k) takes on nearly identical numeral values for different initial values of energy class k ₀ (8 ≤ k ₀ ≤ 12) f(k ₀). The difference decreases with an increasing number of events. We put forward the hypothesis that the values of f(k ₀) tend to cluster around the value 2/3 as the number of events increases. The Kolmogorov test is used to test the hypothesis that statistical recurrence laws are consistent with the analytical form of the probabilistic RR based on a distribution function with the initial value f(k ₀) = 2/3. We discuss statistical distributions of earthquake hypocenters over depth and the epicenters over various areas for several periods     

Study on seismic performance enhancement in bridges based on factorial analysis

The seismic performance of bridges depends on the ductile behavior of its column, as the deck and other substructural components except pile foundations are normally designed to be elastic to facilitate bridge retrofitting.Codes such as AASHTO, Caltrans, IRC: 112 etc.give guidelines for the seismic performance enhancement of columns through ductile detailing.In the present study, a methodology for the seismic performance enhancement of bridges is discussed by using a "Parameter-Based Influence Factor"(PIF) developed from factorial analysis.The parameters considered in the factorial analysis are: percentage of longitudinal reinforcement(P_t), compressive strength of concrete(f'_c), yield strength of steel(f_y), spacing of lateral ties(S) and column height(H).The influence of each parameter and their combination on the limit states considered is estimated.Pushover analysis is used to evaluate the capacity of columns, considering shear failure criteria.A total of 243(3~5 combinations) analysis results are compiled to develop ‘PIF’ used in the performance enhancement process.The study also encompasses other sub-objectives such as evaluating the discrepancies in using the Importance Factor(I) in designing bridges of varied functional importance; and estimating the aspect ratio and slenderness ratio values of bridge columns for its initial sizing.     

Effect of the spectral shape of ground motion records on the collapse fragility assessment of degrading SDOF systems

The main purpose of this paper is to study the collapse capacity of single degree of freedom(SDOF) systems and to produce fragility curves as well as collapse capacity spectra while considering a broad range of structural parameters, including system degradation, the P-Δ effect, ductility capacity and the post-capping stiffness ratio. The modified IbarraKrawinkler deterioration model was used to consider hysteretic behavior. A comprehensive study was conducted to extract the collapse capacity spectrum of SDOF systems with a wide range of periods, varying from 0.05 to 4 s, to cover short, intermediate and long periods. Incremental dynamic analysis(IDA) was performed for SDOF systems to identify the condition in which the collapse capacity of the system is determined. The IDAs were performed using different sets of seismic ground motions. The ground motion records were categorized into different sets based on three spectral shape parameters, including the epsilon, Sa Ratio and N_p. The collapse fragility curves of SDOF systems with different periods were extracted to illustrate the collapse capacity at different probability levels. The results show that structural degradation and ductility as well as the spectral shape parameters significantly affect the collapse capacity of SDOF systems. On the other hand, the post-capping stiffness ratio and small levels of the P-Δ effect do not remarkably change collapse capacity. Also, the collapse capacity of SDOF systems is more sensitive to the records categorized based on Sa Ratio and N_p than those classified based on epsilon.     

Probabilistic performance assessment of low‐ductility reinforced concrete frames retrofitted with dissipative braces

The paper illustrates a probabilistic methodology for assessing the vulnerability of existing reinforced concrete (RC) buildings with limited ductility capacity retrofitted by means of dissipative braces. The aim is to highlight the most important parameters controlling the capacity of these coupled systems and specific aspects concerning the response uncertainties. The proposed methodology is based on the use of local engineering demand parameters for monitoring the seismic response and on the development of component and system fragility curves before and after the retrofit. In the first part of the paper, the methodology is illustrated by highlighting its advantages with respect to the existing approaches. Then, its capability and effectiveness are tested by considering a benchmark two‐dimensional RC frame designed for gravity‐loads only. The frame is retrofitted by introducing elasto‐plastic dissipative braces designed for different levels of base shear capacity. The obtained results show the effectiveness of the methodology in describing the changes in the response and in the failure modalities before and after the retrofit, for different retrofit levels. Moreover, the retrofit effectiveness is evaluated by introducing proper synthetic parameters describing the fragility curves and by stressing the importance of employing local engineering demand parameters (EDPs) rather than global EDPs in the seismic risk evaluation of coupled systems consisting in low‐ductility RC frames and dissipative braces. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic design factors for RC special moment resisting frames in Dubai, UAE

This study investigates the seismic design factors for three reinforced concrete (RC) framed buildings with 4, 16 and 32-stories in Dubai, UAE utilizing nonlinear analysis. The buildings are designed according to the response spectrum procedure defined in the 2009 International Building Code (IBC’09). Two ensembles of ground motion records with 10% and 2% probability of exceedance in 50 years (10/50 and 2/50, respectively) are used. The nonlinear dynamic responses to the earthquake records are computed using IDARC-2D. Key seismic design parameters are evaluated; namely, response modification factor (R), deflection amplification factor (Cd), system overstrength factor (Ωo), and response modification factor for ductility (Rd) in addition to inelastic interstory drift. The evaluated seismic design factors are found to significantly depend on the considered ground motion (10/50 versus 2/50). Consequently, resolution to the controversy of Dubai seismicity is urged. The seismic design factors for the 2/50 records show an increase over their counterparts for the 10/50 records in the range of 200%-400%, except for the Ωo factor, which shows a mere 30% increase. Based on the observed trends, period-dependent R and Cd factors are recommended if consistent collapse probability (or collapse prevention performance) in moment frames with varying heights is to be expected.     

反复荷载下混凝土框架柱塑性铰区基于延性的抗剪承载力机理分析

在试验研究的基础上,以框架结构延性设计为目的采用桁架＋拱模型研究了框架柱塑性铰区域抗剪受力机理,分析了,位移延性系数、加载循环次数等因素对框架柱构件塑性铰区域剪切受力性能的影响,并结合试验结果提出了混凝土框架柱塑性铰区域剪切承载力抗震延性设计实用公式,可有效实现结构的延性破坏机制。主要为配合GBJ10-89的修订,该成果已被《混凝土结构设计规范》（GB50010—2003）吸收。